1. Field of the Invention
The present invention relates to a negative impedance converter, which can make a desired kind of negative impedance conversion by widening the available range of a generalized impedance converter.
2. Description of the Related Art
An impedance converter makes conversion between different impedances in addition to the same impedances. A generalized impedance converter is given as the conventional impedance converter. (For example, see A. Antoniou, “Realization of Gyrators Using Operational Amplifiers, and Their Use in RC Active Network Synthesis”, Proc. IEE, vol. 116, pp. 1838–1850, 1969) The generalized impedance converter comprises a circuit ZIC combining two operational amplifiers Q1, Q2 and four impedance elements Z1 to Z4, as seen from the dashed line frame in FIG. 6. The input impedance Z11′ to convert the negative impedance Z5 is expressed by the following equation (1).                               Z          11                =                                                            Z                1                            ⁢                              Z                3                                                                    Z                2                            ⁢                              Z                4                                              ⁢                      Z            5                                              (        1        )            
More specifically, various impedance elements are used as four impedance elements Z1 to Z4. By doing so, the foregoing generalized impedance converter ZIC can make various impedances proportional to the magnitude of the negative impedance Z5. For example, when the impedance element Z4 is set as capacitor, the impedance is 1/sC4. Further, when impedance elements Z1 to Z3 are individually set as the same resistor R1, and the negative impedance Z5 is set as resistor R2, the input impedance Z11′ is expressed by the following equation (2).Z11′=sR1R2C4  (2)
Therefore, inductor is equivalently obtained.
In addition, when impedance elements Z1 and Z5 are set as capacitors C1 and C5, respectively, the impedance is 1/sC1, 1/Cs5; in this case, the input impedance Z11′ is expressed by the following equation (3).                               Z                      11            ′                          =                  1                                    s              2                        ⁢                          R              1                        ⁢                          C              1                        ⁢                          C              5                                                          (        3        )            
If s=jω (ω=2πf), the following equation (4) is obtained.                                           Z                          11              ′                                ⁡                      (                          j              ⁢                                                          ⁢              ω                        )                          =                              -            1                                              R              1                        ⁢                          C              1                        ⁢                          C              5                        ⁢                          ω              2                                                          (        4        )            
The polarity of the input impedance Z11′ is negative; therefore, a negative resistor called frequency-dependent negative resistor (FDNR) is obtained. In this case, the frequency-dependent negative resistor (FDNR) has property inversely proportional to ω2, that is, frequency f. Thus, the frequency-dependent negative resistor (FDNR) is applicable as a new ladder-type filter.
As described above, the conventional generalized impedance converter can make mutual conversion between different impedance as capacitor and inductor, and negative resistor inversely proportional to ω2.
However, the conventional generalized impedance converter cannot make negative capacitor and negative inductor.
The present invention has been made in view of the foregoing circumstances. It is, therefore, an object of the present invention to provide a negative impedance converter, which readily can obtain negative capacitor and negative inductor in addition to negative resistor by widening the available range using a generalized impedance converter circuit.